Tanh[a]^2 - Tanh[b]^2 == Sech[a]^2 Sech[b]^2 Sinh[a - b] Sinh[a + b]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msup> <mi> tanh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <msup> <mi> tanh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sech </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <power /> <apply> <tanh /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <tanh /> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <sech /> <ci> a </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <sech /> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <sinh /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["Tanh", "[", "a_", "]"]], "2"], "-", SuperscriptBox[RowBox[List["Tanh", "[", "b_", "]"]], "2"]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox[RowBox[List["Sech", "[", "a", "]"]], "2"], " ", SuperscriptBox[RowBox[List["Sech", "[", "b", "]"]], "2"], " ", RowBox[List["Sinh", "[", RowBox[List["a", "-", "b"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", "+", "b"]], "]"]]]]]]]]

2001-10-29